diff --git a/pkg/block/index.go b/pkg/block/index.go
index eb0a3689c0..232bf40d37 100644
--- a/pkg/block/index.go
+++ b/pkg/block/index.go
@@ -347,7 +347,7 @@ func GatherIndexIssueStats(logger log.Logger, fn string, minTime int64, maxTime
 		}
 		l0 := lset[0]
 		for _, l := range lset[1:] {
-			if l.Name <= l0.Name {
+			if l.Name < l0.Name {
 				return stats, errors.Errorf("out-of-order label set %s for series %d", lset, id)
 			}
 			l0 = l
diff --git a/pkg/compact/compact_e2e_test.go b/pkg/compact/compact_e2e_test.go
index 11213dc047..dc6c7c1fd3 100644
--- a/pkg/compact/compact_e2e_test.go
+++ b/pkg/compact/compact_e2e_test.go
@@ -180,7 +180,7 @@ func TestGroup_Compact_e2e(t *testing.T) {
 		extLset := labels.Labels{{Name: "e1", Value: "1"}}
 		b1, err := testutil.CreateBlock(prepareDir, []labels.Labels{
 			{{Name: "a", Value: "1"}},
-			{{Name: "a", Value: "2"}},
+			{{Name: "a", Value: "2"}, {Name: "a", Value: "2"}},
 			{{Name: "a", Value: "3"}},
 			{{Name: "a", Value: "4"}},
 		}, 100, 0, 1000, extLset, 124)